1. Chapter 5 Topology Control
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2. Outline 5.1. Motivations and Goals
5.2. Power Control and Energy Conservation
5.3. Tree Topology
5.4. k-hop Connected Dominating Set
5.5. Adaptive node activity
5.6. Conclusions
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3. Outline 5.1. Motivations and Goals
5.2. Power Control and Energy Conservation
5.3. Tree Topology
5.4. k-hop Connected Dominating Set
5.5. Adaptive node activity
5.6. Conclusions
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4. Motivations A typical characteristic of wireless sensor networks
deploying many nodes in a small area
ensure sufficient coverage of an area, or
protect against node failures
Networks can be too dense: too many nodes in close (radio) vicinity
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5. Motivations In a very dense networks, too many nodes
Too many collisions
Too complex operation for a MAC protocol
Too many paths to be chosen from for a routing protocol, …
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6. Goals This chapter looks at methods to deal with such networks by
Reducing/controlling transmission power
Deciding which links to use
Turning some nodes off
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7. Topology Control Topology control: Make topology less complex
Which node is able/allowed to communicate with which other nodes
Topology control needs to maintain invariants, e.g., connectivity
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8. Options for topology control
Flat network
All nodes have essentially same role
Hierarchical network
Assign different roles to nodes and then control node/link activity
Dominating sets
Tree
Adaptive node activity
Hybrid
Power control
Clustering
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9. Outline 5.1. Motivation and Goals
5.2. Power Control and Energy Conservation
5.3. Tree Topology
5.4. k-hop Connected Dominating Set
5.5. Adaptive node activity
5.6. Conclusions
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10. Introduction of Power Control
The transmitter’s power can be adjusted dynamically over a wide range
Typical radio adjusts their transmitter’s power based on received signal strength A C
Connected
Disconnected B A
Power control之定義與介紹，傳送電量可以動態地調整，並且透過調整電量來達到增加傳輸距離之能力，通常傳輸電量之調整是依據接收訊號強度進行微調。Power control對於整個網路之影響具有全域性，即代表一個node調整他的傳輸電量會影響其它node之傳送與接收，故在所有node之全域最佳解，可以在trade-off之策略下找出最佳解。
左圖所示為當node B、node D皆與其它node斷路而無法通訊，當node A加大其傳輸功率，藉此達到增加傳輸距離之效果，此時node D、node B與其它連通，即可互相收送資料，整個網路才視為連通。
Power control之特性有控制傳輸之功率、路徑控制以及增加網路連通性、路徑維護與網路修復、收集鄰居資訊等。
Controls the transmission power
Topology control for desired connectivity
Compensate topology changes incurred by mobility and dead nodes D
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11. Introduction of Power Control
Interactions
Power control
Large Battery makes
Longer Lifetime
Power control所影響之參數非常多，如圖所示我們可以發現，power control對干擾、連通性、電量、錯誤傳輸率以及空間利用度皆有影響。
Battery drain
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12. Introduction of Power Control
Interactions B A C
Interference
Large Power makes
Performance Degradation D
Source
Destination
Power control
Power control所影響之參數非常多，如圖所示我們可以發現，power control對干擾、連通性、電量、錯誤傳輸率以及空間利用度皆有影響。
Large Battery makes
Longer Lifetime
Battery drain
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13. Introduction of Power Control
Interactions B A
Interference C
Large Power makes
Performance Degradation
Source D
Destination
Power control
Different Power makes
Load Unbalancing
Power control所影響之參數非常多，如圖所示我們可以發現，power control對干擾、連通性、電量、錯誤傳輸率以及空間利用度皆有影響。
Large Battery makes
Longer Lifetime D
Destination C B
Adjusting power can balance the power consumption A
Source
A consumes much more power than C
Battery drain
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14. Introduction of Power Control
Interactions
Adjusting the power of A can improve the spatial reuse
C is forbid to communication with B B B C A D
Interference C A E
Large Power makes
Performance Degradation
Small Power creates more
Spatial Reuse Opportunities
Source D
Destination
Power control
Different Power makes
Load Unbalancing
Power control所影響之參數非常多，如圖所示我們可以發現，power control對干擾、連通性、電量、錯誤傳輸率以及空間利用度皆有影響。
Large Battery makes
Longer Lifetime C A D
Destination B
Source
A consumes much more power than C
Battery drain
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15. Introduction of Power Control
Interactions
Adjusting the power of A can improve the spatial reuse B B C A D
Interference C A E
Large Power makes
Performance Degradation
Small Power creates more
Spatial Reuse Opportunities
Source D
Destination
Power control
Different Power makes
Load Unbalancing
Small Power causes
More Retransmissions
Power control所影響之參數非常多，如圖所示我們可以發現，power control對干擾、連通性、電量、錯誤傳輸率以及空間利用度皆有影響。
Large Battery makes
Longer Lifetime C
Error rate A D
Destination
Error performance B
Large power, small error rate
Source
A consumes much more power than C
Battery drain
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16. Introduction of Power Control
Targets and Issues
Improve network throughput
Improve transmission range
Improve fairness
Improve connectivity
Power control helps in scheduling
Reduce the interference and energy consumption
Partial combination of above targets
etc.
使用power control的目的有增加網路之效率、增加傳輸範圍、增加公平性與連通性等，power control一直為ad-hoc中相當重要的研究。
我們好奇的問題是power control如何增加網路之效能? 例如增加傳輸功率以降低重傳機率、透過功率調整以增加空間利用度、增加傳輸功率以增加傳輸資料量等。
以下將分別介紹這方面相關的研究。
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17. Power Control and Energy Conservation
Topology Control of Multihop Wireless Networks using Transmit Power Adjustment
R. Ramanathan and R. Rosales-Hain
IEEE INFOCOM 2000
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18. Introduction Topology
The set of communication links between node pairs used by routing mechanism
Uncontrollable factor: mobility, weather, interference, noise
Controllable factor: transmission power, antenna direction
可控制Topology的參數，以及不可控制Topology的參數
本篇Paper針對Transmit power參數做討論
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19. Introduction
A graph is called connected if every pair of distinct vertices in the graph can be connected through some path
A bi-connected graph is a connected graph that is not broken into disconnected pieces by deleting any single vertex (and its incident edges)
Connected
Bi-connected
Connected 及 bi-connected graph 性質介紹
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20. Motivation Drawbacks of wrong topology Sparse network Dense network
Reduce network capacity
Increase interference
Increase end-to-end packet delay
Sparse network
A danger of network partitioning
High end to end delays
Dense network
Many nodes interfere with each other
動機 :
1. 不好的Topology所造成的缺點，Reduce the capacity，Increase interference 及 Increase end-to-end packet delay
2. 所以本論文欲建立一好的 network topology
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21. Static Networks: Min-Max Power Algorithm
Goal
Find a per-node minimal assignment of transmitted power p
such that (1) the induced graph is connected and (2) max p is minimum
Min-Max Power Algorithm – Connected Networks
目標 :
Network 形成 connected topology
使每個節點的 power 為最小
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22. Min-Max Power Algorithm- Connected Networks
Phase I: CONNECTION
Construct a Minimum cost spanning tree A B C D E F 2 1 3
Successful transmit power
between i and j 3 3 4
s : the receiver sensitivity
Phase I: CONNECTION
將 network 轉為圖論 :
節點為 sensor ，且其與周圍鄰居通訊所要打的 power，可經由彼此的距離計算求得最小的 power 應該為多少。Successful transmit power 是最小可成功傳送之power，為 path loss + 接收者可成功接收資料的最小訊號強度
邊上之 weight 為兩節點可通訊的最小 power
由 Minimum cost spanning tree，找出最低成本的 Connected topology 1 1
: path loss between i and j
: the location of node i 2
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23. Min-Max Power Algorithm- Connected Networks
Phase II : Per Node Minimizing Power
side-effect-edge :
The edge of (C, D) is automatically
connected A B C D E F 2 1 3 3 3 4
A has a path to B via C with smaller power
→A adjusts the transmitted power from 2 to 1.
B has a path to A via D with smaller power
→B adjusts the transmitted power from 2 to 1.
Phase II: Per Node Minimizing Power
雖然 side-effect-edge 不是我們所建立的邊，但是其兩端節點卻是可以通訊的。
因此，A 與 B 可檢查是否可縮小其 power ，而且 network 仍是 Connected
例子1，A 與 B可經由A->C->D->B路徑連通，因此A可縮小Power 為 1，並 disconnect AB之間的 link
4. 同理，B亦相同 1 1 1 2 1
The edge (A, B) can be disconnected to save more energy
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24. Min-Max Power Algorithm- Bi-Connectivity Augmentation
Phase I: BICONN-AUGMENT
Construct a Connected Minimum cost spanning tree A B C D E F 2 1 3
Successful transmit power
between i and j 3 3 4
s : the receiver sensitivity
Phase I: BICONN-AUGMENT
1. 同 “Min-Max Power Algorithm – Connected Networks” 將 network 轉為圖論 :
2. 首先建立一 Connected Minimum cost spanning tree graph G 1 1
: path loss between i and j
: the location of node i 2
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25. Min-Max Power Algorithm- Bi-Connectivity Augmentation
Phase I: BICONN-AUGMENT
Add (u, v) to graph G until the network is bi-connected
Bi-Connected component of C
Bi-Connected component of D A B C D E F 2 1 3 4 D F C E A C B D
加入新的邊，使G 成為Bi-Connectivity graph:
依序檢查是否加入weight最小的邊，直到G為 bi-connectd 為止
1.檢察邊 (C, D) ，因為 biconn-comp (G, C) 不等於 biconn-comp (G, D)，因此加入邊 (C, D) 到 G
Bi-Conn. Comp. of C  Bi-Conn. Comp. of D
=> Add (C, D)
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26. Min-Max Power Algorithm- Bi-Connectivity Augmentation
Phase I: BICONN-AUGMENT
Add (u, v) to graph G until the network is bi-connected
Bi-Connected component of E
Bi-Connected component of F A B C D E F 2 1 3 4 D F C E
2. 接著檢驗邊 (E, F) ，因為 biconn-comp (G, E) 不等於 biconn-comp (G, F)，因此加入邊 (E, F) 到 G
最後，所有邊均檢查過後，且G為 Bi-Connectivity graph ，則 Phase I 演算法結束
Bi-Conn. Comp. of E  Bi-Conn. Comp. of F
=> Add (E, F)
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27. Min-Max Power Algorithm- Bi-Connectivity Augmentation
Phase II: Per Node Minimizing Power
No side-effect-edge →Finish A B C D E F 2 1 3 4
Phase II: Per Node Minimizing Power
沒有 side-effect-edge，結束 Phase II 演算法
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28. Min-Max Power Algorithm- Bi-Connectivity Augmentation
Phase II: Per Node Minimizing Power
An other example has side-effect-edge
side-effect-edge :
The edge of (A, D) is automatically
connected 2 3 1 3 1 B A 3 3 3 2
Phase II: Per Node Minimizing Power:
舉例有 side-effect-edge 的例子
(A，D)為 side-effect-edge，A與D可通訊
Node C 可調整自己power為2，並 disconnect 邊 (A, C) ，且 G 仍為 Bi-Connectivity D C 3 2 2
Disconnect the edge (A, C) and still Bi-Connectivity
→C adjusts the transmitted power from 3 to 2
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29. Min-Max Power Algorithm- Bi-Connectivity Augmentation
Phase II: Per Node Minimizing Power
An other example has side-effect-edge
Disconnect the edge (B, D) and still Bi-Connectivity
→B adjusts the transmitted power from 3 to 2 2 1 3 3 2 A 1 B 3 2 3 3
3. Node B 可調整自己power為2，並 disconnect 邊 (B, D) ，且 G 仍為 Bi-Connectivity D C 2 3
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30. Min-Max Power Algorithm- Bi-Connectivity Augmentation
Phase II: Per Node Minimizing Power
Finish 1 2 3 A B C D
所有 node 執行完 Per Node Minimizing Power 演算法縮小 power 後，產生最後結果 G 且 Bi-Connectivity
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31. Outline 5.1. Motivation and Goals
5.2. Power Control and Energy Conservation
5.3. Tree Topology
5.4. k-hop Connected Dominating Set
5.5. Adaptive node activity
5.6. Conclusions
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32. Introduction of Tree Topology Control
Example:
MPR (Multi-Point Relay) election
Retransmission node
Retransmission node
(b)
在此為一個例子，其中我們可以看到左圖因為沒有由root建立tree，造成許多節點收到資料就直接傳送出去，使得過多的重傳次數，讓電量消耗增加。
右圖則由root到leaf建立tree，讓重傳的次數降低，使得整個網路的life time增加。
但如何選擇這些relay node則是非常重要的問題，常見的做法有spanning tree。
(a)
(b) is better than (a)
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33. Introduction of Tree Topology Control
Example: g h a b c d e f g h a b c d e f
通常在方面的問題會使用spanning tree來管理網路，這是由於spanning tree的特性可以建出最短路徑樹，可以減少傳輸的hop數，進而減少所需消耗的電量，
我們可以看到左圖為集中式的做法，由root進行BFS即可得到一個spanning tree，此種做法可以得到較好的網路效率。
右圖為分散式的建立方法，此為一個worst case，可能建出非BFS的tree，造成過多的傳輸步數，其中可以發現a->d要傳輸7 hops，故分散式的做法有較高的困難度及研究價值，以下將分別介紹這方面相關的研究。
(a)
(b)
a to d needs 2 hops
a to d needs 7 hops
(a) is better than (b)
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34. Design and Analysis of an MST-Based Topology Control Algorithm
Tree Topology
Design and Analysis of an MST-Based Topology Control Algorithm
N. Li, J. C. Hou, and L. Sha
IEEE INFOCOM 2003
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35. Motivation The advantage of Topology Control
Minimize the overhearing and then optimize the network spatial reuse
Maintain a connected topology by minimal power
Power-efficient A B C D E F G H I
(2) With Topology Control A B C D E F G H I
動機：
有拓墣控制可以有以下優點:
1.最小化overhearing進而佳化網路空間的利用性.
2.同時,以最小電量維持網路的連通性.
2.省電
如圖一:
令節點與節點之間的連線表彼此間可通訊.
假設節點A&D有資料需要傳輸,
則因為B C E F G I將overhear到A&D之間的傳輸,
而為了不使A&D傳輸失敗,所以將不能有任何溝通之行為,
如此便沒有上述之優點.
反之,圖二因為有拓墣控制,
所以A與D之間的溝通並不會影響到其它的節點,
因此會有上述之優點.
(1) No Topology Control
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36. Goal Determine the transmission power of each node
Maintain network connectivity
Minimal power consumption
目標：
每一個節點都能夠算出與個別鄰居間的傳送電量
1.能夠維持網路的連通性
2.且是利用最小的傳送電量來達成
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37. Local Minimum Spanning Tree Algorithm (LMST)
Step 1: Information Collection
Step2: Topology Construction
Step3: Determination of Transmission Power
解決方法：
[區域的最小成本展開樹演算法] 分為以下三階段:
步驟1. 資訊收集
步驟2. 拓樸建置
步驟3. 計算傳送電量
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38. LMST – Step1: Information Collection
Information Exchange
Each node broadcasts periodically a Hello message using its maximal transmission power.
The Hello message includes the ID and Location of the node.
u‘’s ID and Location c a u b d
Maximal Transmission Power
資訊交換階段：
1.每個節點週期性地使用最大傳送電量廣播Hello message.
2.其中，Hello message包含了該結點的ID及位址.
3.週期性地傳遞Hello message的時間區間大小是依據節點的移動性等級來介定
動畫:
以下的步驟是每一個節點都會同時各自做,
以u節點來講解:
u節點以最大的communication半徑所圍的sensing range內,
a, b, c, d節點都是u節點所能直接溝通的節點,
接著u節點會週期性地發送Hello Message給這些節點,
而Hello Message內容包含自己的id以及位址.
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39. LMST – Step1: Information Collection
Information Exchange
Since Hello message includes the node’s ID and Location, after obtaining the Hello message of 1-hop neighbors, node u can construct the local view. c a u b d
資訊交換階段：
在u節點得到了一步鄰居的ID與位址後,
可以建置自己的local view.
動畫:
u節點的local view如動畫所示.
以上為Information Collection的階段.
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40. LMST – Step2: Topology Construction
The weight of edge between the two nodes is based on Euclidean distance.
The weight of an edge also denotes the transmission power (or distance) between the two nodes c a u b d e 3 4 5 6 7 10
c ： Coefficient
d ： distance
拓樸建置階段
1.首先,兩節點之間會建立連線成為邊,而此邊代表的是transmission power的權重邊
2.其權重邊的大小是依據兩節點間Euclidean距離所計算,
而下面的公式所代表的意思為:
Sensing Range要為為先的兩倍,則power則要加大到原先power的平方倍才能達到相同的訊號強度.
也就代表說:
減小的transmission range,所節省下來的power是平方倍觀距離的.
3.接著,每一個節點都需個別地應用Prim演算法建置區域的最小成本展開樹.
動畫為一個以Prim’s 演算法建立的Local Minimum Spanning Tree (LMST)的例子:
令節點與節點之間的連線為彼此可以直接通訊的邊,
以下步驟為每一個節點都會同時間的做,這裡以u節點為例,
一開始以u節點為初始節點,在可以與u節點直接通訊的邊之中,
選定Euclidean distance最小的為最小成本邊,也就是 u<->c,
接著可以與u與c節點直接通訊的邊之中再挑選最小成本邊,也就是c<->d,
以次類推, u<->b, b<->a, b<->e依序被挑選為最小成本邊,
最後所形成的紅色邊連線為u節點的LMST.
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41. LMST – Step 2: Topology Construction
Each node applies Prim’s algorithm independently to obtain its Local Minimum Spanning Tree.
Node u constructs the Local Minimum Spanning Tree using Prim’s algorithm according to its local view
local view of node u
According to the constructed Local Minimum Spanning Tree, node u will use small power to communicate with node a via node b instead of using large power to communicate with node a directly. 7 e a 5
拓樸建置階段
每個Node應用Prim的演算法建立自己的最小成本樹.
動畫:
為一個以Prim’s 演算法建立的Local Minimum Spanning Tree (LMST)的例子:
令節點與節點之間的連線為彼此可以直接通訊的邊,
以下步驟為每一個節點都會同時間的做,這裡以u節點為例,
一開始以u節點為初始節點,在可以與u節點直接通訊的邊之中,
選定Euclidean distance最小的為最小成本邊,也就是 u<->c,
接著在可以與u與c節點直接通訊的邊之中,再挑選最小成本邊,也就是u<->b,
以次類推,b<->a被挑選為最小成本邊,
最後所形成的紅色邊連線為u節點的LMST.
黃色框框
在建立完最小成本樹之後,
節點u要與節點a溝通須透過建立後的拓樸的路線來溝通,
也就是需要透過節點b.
綠色框框
根據上述方式,可以將節點u的電量消耗平均分散,
又可以增加更多的Spatial Reuse機會. 6 7 b 10 5 u 7
Small power:
Creates more spatial reuse opportunity
Decreases energy consumption 6 3 c 4 d
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42. LMST – Step 3: Determination of Transmission Power
By measuring the receiving power of Hello message, each node can determine the specific power levels it needs to reach each of its neighbors.
Two commonly-used propagation models
Free Space
Two-Ray
Sign
Meaning Pt
Transmit power Pr
Receive power Gt
Antenna gain of the transmitter Gr
Antenna gain of the receiver 
Wave length d
Distance between nodes L
System loss ht
Antenna height of the transmitter hr
Antenna height of the receiver
決定傳送電量階段
在LMST建立之後,每一個節點要與其他節點通訊就要以此公式來計算需要傳送的電量
1.藉由收到Hello message的電量，每個節點可以算出與鄰居間要傳送接收的最小電量.
2.兩個常被使用的傳播模型:Free Space及Two-Ray
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43. LMST – Step 3: Determination of Transmission Power
In general, the relation between Pr and Pt is of the following form
Where G is a function of
Example
Pth is the required power threshold to successfully receive the message
Pmax is the maximal transmission power e
Node b will compute： a
2.例子:
在資訊交換階段,節點b收到節點u以最大電量打的Hello message,
節點b將會依據收到的Pr用來計算G
G = Pr / Pmax (Pmax為最大電量)
3.因此,當節點b需要傳送資料至節點u時,
只需要打電量為以下式子:
Pth * G = PthPr / Pmax (Pth為使節點u正確的了解訊息的電量臨界值) b
Hello
Data
Node b transmits data to u：
Data with PthG u c d
Hello with Pmax
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44. Conclusions Advantages
Maintain network connectivity by low energy consumption
Reduce the probability of interference
Increase the spatial reuse
Achieve high throughput
優點:
1.全域的連接性
2.不需要每次都用最大的POWER打出去,而是經由計算的最小POWER,所以省電!
3.因為POWER的大小是根據要溝通鄰居的距離而定,因此減少讓無關的節點overhearing,因此Low interference!
4.增加了spatial reuse, 因此throughput也因此增加!
2017/4/24

45. J. Wieselthier, G. Nguyen, and A. Ephremides
Tree Topology
On the Construction of Energy-Efficient Broadcast and Multicast Trees in Wireless Networks
J. Wieselthier, G. Nguyen, and A. Ephremides
IEEE INFOCOM 2000
2017/4/24

46. Introduction
The paper studies the problems of broadcasting and multicasting in wireless networks.
To form a minimum-energy tree
Energy efficiency
Maintain network connectivity
這篇paper主要是在無線網路場景中，建立一有效率的brocasting tree 動機
先前文獻中，針對建立multicasting tree都是以link-based models 進行探討，然而，本篇論文作者認為，這樣的model是無法完全套用在無線網路的場景中。
2017/4/24

47. Network Assumptions
The power level of a transmission can be chosen within a given range of values.
The availability of a large number of bandwidth resources.
Sufficient transceiver resources are available at each of the nodes in the network.
PAPER假設
1.傳送者可以控制傳送範圍的大小
2.有大量頻寬資源可使用
3.能夠同一時間接收多筆不同的資料
2017/4/24

48. Wireless Communications Model
Node-based transmission cost evaluation
Pi,(j,k) = max{Pij, Pik},
Pij : Transmission power for node i to transmit packets to node j
The larger power (Pik ) can cover both of node j and node k
Pik > Pij j
Pij
Pij表示節點i到節點j所花費的電量(※α為與power成正比的值，α is a parameter that typically takeson a value between 2 and 4)
假設source為i ,destination為j及k
i傳送資料到j縮需之power為Pij
i傳送資料到k縮需之power為Pik
i若以Pij的power傳送資料時，則只有j點收到資料
相反地，i若以Pik的power傳送資料時，則j及k都能收到資料
因此，我們利用上述符號Pij，我們取Pi,(j,k) = max{Pij, Pik}計算Node-based(無線網路)的成本，　
The smaller power (Pij ) can only cover node j i
Pik k
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49. The Broadcast Incremental Power Algorithm5 g
Assume node a is the source node
Step 1: Determining the node that the Source can reach with minimum expenditure of power. f 4
1.5
1.3
1.2
1.7 3 a b h d
0.3
0.9 1 c
0.5 2
1.3
0.8
BIP做法
存在10個節點在網路場景，編號ａ的節點為起點
A propagation constant of α = 2
開始建樹
Step 1. 起點挑選最近之節點建立連線，因此，節點ａ選取節點ｂ
1.1
0.7 j i e
0.3 1 a b
0.5 a c 1 2 3 4 5
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50. The Broadcast Incremental Power Algorithm
Step 2: Determine which “new” node can be added to the tree at minimum additional cost. 5 g f 4
1.5
1.3
ΔPa
1.2
1.7
0.5 a c
Pac 3 a Pa
0.3 a b b h d
0.3
0.9
ΔPa = 0.5 – 0.3 = 0.2 1 1 c
0.5
Minimum additional cost 2
1.3
0.8
Step 2.接著再選取下一個最小成本之節點
此時，投影片上的例子有兩種情況
　　　(1).節點ａ加大他的POWER至節點ｃ
(2).節點ｂ選取最近之節點加入
從上述兩種情況中，選一最小成本之節點加入樹，我們以下列例子說明如何選出最小成本之節點加入樹。
首先以Pab及Pbd來做比較，其中計算方式如下:
我們以Pab來看的話…
Pac為節點a傳送到節點c所需的cost(例:節點a與節點c溝通所須的transmission power為0.5)
Pa為節點a先前決定的POWER大小(如:節點a為0.3，節點b為0)
ΔPa為節點a所需增加的cost大小,(例如:在前一STEP，節點a的transmission power為0.3，因此，若節點a想將直接與c節點通訊(須花費0.5)，但實際上power只須再增加0.2即可(ΔPa=0.2))
ΔPa＝Pac-Pa
然而，Pbd也做同一個計算
再比較ΔPi取最小值為我們所要的最小成本之節點(這個例子我們會選Pac的方式加入樹)
1.1
0.7 j
ΔPb i e 1 1 b d
Pbd Pb b
ΔPb= 1 – 0 = 1 1 2 3 4 5
2017/4/24

51. The Broadcast Incremental Power Algorithm
Step 2: Determine which “new” node can be added to the tree at minimum additional cost. 5 g f
ΔPa 4
1.3 a j
Paj
1.5
1.3
1.2
1.7 Pa
0.5 a c 3 a
ΔPa = 1.3 – 0.5 = 0.8 b h d
0.3
0.9
ΔPc 1 c
0.5
0.7 c j
Pcj 2
1.3
0.8
a－j、c－j、b－d三者比較後，加入c－j所增加的cost最小
Step 2.接著再選取下一個最小成本之節點
此時，投影片上的例子有兩種情況
　　　(1).節點ａ加大他的POWER至節點ｃ
(2).節點ｂ選取最近之節點加入
從上述兩種情況中，選一最小成本之節點加入樹，我們以下列例子說明如何選出最小成本之節點加入樹。
以Paj及Pcj及Pbd來做比較，其中計算方式如下:
我們以Pab來看的話…
Paj為節點a傳送到節點c所需的cost(例:節點a與節點c溝通所須的transmission power為1.3)
Pa為節點a先前決定的POWER大小(如:節點a為0.5，節點b及c為0)
ΔPa為節點a所需增加的cost大小,(例如:在前一STEP，節點a的transmission power為0.5，因此，若節點a想將直接與j節點通訊(須花費1.3)，但實際上power只須再增加0.8即可(ΔPa=0.2))
ΔPa＝Pac-Pa
然而，Pbd及Pcj也做同一個計算
再比較ΔPi取最小值為我們所要的最小成本之節點(這個例子我們會選Pcj的方式加入樹)
1.1
0.7 Pc c
Minimum additional cost j i e
ΔPc = 0.7 – 0 = 0.7 1
ΔPb 1 b d
Pbd Pb b 1 2 3 4 5
ΔPb = 1 – 0 = 1
2017/4/24

52. The Broadcast Incremental Power Algorithm5 g
Step 2: Determine which “new” node can be added to the tree at minimum additional cost. f 4
1.5
1.3
1.2
1.7
And so forth：
c → i
c → h
b → d
b → e
b → f
b → g 3 a b h d
0.3
0.9 1 c
0.5 2
1.3
0.8
以此類推，加入c → i, c → h, b → d, b → e, b → f, b → g
1.1
0.7 j i e 1 1 2 3 4 5
2017/4/24

53. The Broadcast Incremental Power Algorithm
BIP is similar in principle to Prim’s algorithm.
One fundamental difference:
The inputs to Prim’s algorithm are the link cost Pij.
BIP must dynamically update the costs at each step.
BIP相似於Prim’s algorithm的原理
其中不太一樣的地方為
Prim’s algorithm以link based的模式運行
BIP在每個step中，更新每個節點的cost
2017/4/24

54. Conclusions
Propose a centralized algorithm: The Broadcast Incremental Power(BIP) Algorithm
Advantages
Improved performance can be obtained when exploiting the properties of the wireless medium
Energy-efficient 優點
1.提升效能
2. Energy-efficient 缺點
1.本篇為一集中式做法，非分散式
2.未考量頻寬的問題
3.未考量接收器不足的問題
以上缺點都有可能影響到本論文機制之結果
2017/4/24

55. Outline 5.1. Motivation and Goals
5.2. Power Control and Energy Conservation
5.3. Tree Topology
5.4. k-hop Connected Dominating Set
5.5. Adaptive node activity
5.6. Conclusions
2017/4/24

56. Connected Dominating Set
Connected dominating set (CDS) - construct a virtual backbone.
Communicate through the virtual backbone by dominators.
Example: virtual backbone construction
Sensor node
未分組前的網路拓樸較複雜，傳播時網路負擔大
2017/4/24

57. Connected Dominating Set
Connected dominating set (CDS) - construct a virtual backbone.
Communicate through the virtual backbone by dominators.
Example: virtual backbone construction
CDS edge
Virtual backbone
Sensor node
Dominators
找出dominating set後，可以大幅簡化網路的topology
1-hop Connected Dominating Set
2017/4/24

58. Connected Dominating Set
Connected dominating set (CDS) - construct a virtual backbone.
Communicate through the virtual backbone by dominators.
Example: virtual backbone construction
CDS edge
Virtual backbone
Sensor node
Dominators
找出dominating set後，可以大幅簡化網路的topology
1-hop Connected Dominating Set
2-hop Connected Dominating Set
2017/4/24

59. A Hardness Result
The MDS (minimum dominating set) problem is NP-hard, it is even a hard problem to approximate in general.
For the case of unit disk graphs, it is possible to find a Polynomial Time Approximation Scheme (PTAS).
MDS problem是一個NP-hard問題，很難求得最佳解
下列幾篇paper將會提出演算法求得近似解
2017/4/24

60. k-hop Connected Dominating Set
On Calculating Power-Aware Connected Dominating Sets for Efficient Routing in Ad Hoc Wireless Networks
Jie Wu, Fei Dai, Ming Gao, and Ivan Stojmenovic
Journal of Communications and Networks 2002
2017/4/24

61. Introduction
Routing based on a connected dominating set is a promising- approach
Each gateway host keeps following information: gateway domain membership list and gateway routing table. 3 10 11
Gateway domain member list of host 8
Gateway host
Non-Gateway host 1 2 5 6 7 4 9 3 8 10 11
dominated set
Receiver
1.用connected dominating set 來解決繞徑的問題是一個不錯的方法,因為可以把網路中某一點傳封包給另一點的問題,簡化為 在集合中找一個node的問題,
2.但用connected dominating set 來解決繞徑的問題,每一個gateway host(在dominating set中的nodes)都需maintain 其gateway domain membership list 和 gateway routing table.舉例來說gateway host 8，他的gateway domain membership list 就是3、10、11。也就是與8相鄰的host中,屬於Non-Gateway host(在dominating set外中的nodes)得那些host.而Gateway routing table包含所有gateway hosts的資訊及其domain member list及其他繞境資訊。
Ex: senser8要傳給receiver5,則透過routing table中的member list得知若要傳給5,則需先傳給next hop : node7,然後7也會有自己的routing table,最後把資料傳給4.
destination
member list
next hop
distance 9
(1,2,3,11) 1 4
(5,6) 7 2
(6)
Gateway routing table of host 8
Sender
2017/4/24

62. Introduction
In order to prolong the life span of each node, power consumption should be minimized and balanced among nodes.
Unfortunately, nodes in the dominating set consume more energy than nodes outside the set.
Propose a method of calculating power-aware connected dominating set based on a dynamic selection process. 5
Gateway host 6 2
Non-Gateway host
Dominated set 7 4
另一方面,為了增加網路的生命週期,應該要盡量平衡各個node間的電量消耗以及最小化整個網路的電量消耗
但是通常在dominating set中的node,會比在set外的node消耗更多的電量,故容易造成電量不平衡(因為代傳較多資料)
所以作者加入電量的計算,希望找出的dominating set中的那些gateway nodes(較易代傳資料的node)是電量較高的,使得網路中電量盡量平衡
Ex:node2和5都透過9和4代傳資料,但由於4的電量較高,之後的做法可能就會將9排除在dominating set之外,只留4! 8 10 9 12 1 11 3
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63. Network Initialization
Every v exchanges its neighbor set N(v) with all its neighbors.
Each node has two-hop neighbors information.
Every v is marked if there exist two unconnected neighbors 1 2 3 5 6 7 8 9 10 4 11 12 13 14 15 16 17 19 20 18 21 22 27 26 24 23
unconnected
Become a Gateway host
1.一開始每個node把自己的鄰居資訊跟自己鄰居講,也就是每個node會擁有兩步鄰居資訊
2.每個node判斷自己鄰居中,是否有任兩個無法直接連接,若有把自mark起來,也就是標為gateway host
以2為例,他鄰居中1和5無法知接通訊,所以2將自己標為gateway host,但這類的node在網路中會有很多,如動畫所示
Non-Gateway host
Gateway host
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64. Gateways Selection (Rules 1 and 2)
所以接下來作者就加入幾個rules來簡化此connected dominated set
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65. Gateways Selection (by applying Rule 1)
Rule 1: Consider two vertices v and u in G’. If N[u]  N[v]in G and id( u ) < id(v), the marker v is unmarked, i.e., G' is changed to G' - {u}. 20 21 22 27 25 24 23 26
N(21)  N(22) id
N(id) 21
22, 23, 24 22
20, 21, 23, 24, 25, 26, 27
Rule1如下所示
直接用例子來說明,node21的鄰居以N[21] 表示,則N[21] = {21,22,23,24}, 而N[22] ={20,21,22,23,24,25,26,27}
明顯的N[21] 包含於N[22],且node21的id小於node22,因此根據 Rule 1,node21會unmark他自己,把他自己當作non-gateway host,如動畫所示
Non-Gateway host
Gateway host
2017/4/24

66. Gateways Selection (by applying Rule 2)
Rule 2: Assume that u and w are two marked neighbors of marked vertex u in G’. If N(u)  N(v)  N(w) in G and id(u) = min{id(v),id(u),id( w)},then the marker of u is unmarked. 1 2 3 5 6 7 8 9 10 4 11
N(2)  N(4)  N(9)
and id(2) = min{id(2), id(4), id(9)}
Non-Gateway host
Gateway host id
N(id) 2
1, 3, 4, 5, 6, 7, 8, 9 4
1, 2, 3, 9, 10, 11 9
2, 4, 5, 6, 7, 8, 10
根據rule2, N[2]包含於 N[4]∪ N[9]. 此外Node 2的id是node2,4,9中最小的,因此
根據 Rule 2,node2會unmark他自己
2017/4/24

67. Extended Rules Several extended approaches for selective removal
The node-degree-based approach aims at reducing the size of the connected dominating set
The energy-level-based approach tries to prolong the average life span of each node.
考慮兩個延伸的規則,一個是base on node degree,另一個base on energy level,(剛剛是base on node id)前者是用來化簡connected dominating set的size,後者用來延長網路lifetime
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68. Node-degree-based Approach (Rule 3)
Rule 3: Consider two marked vertices v and u in G’. The marker v is unmarked if one of the following conditions holds:
N[u]  N[v] in G and nd(u) < nd(v)
N[u]  N[v] in G and id(u) < id(v) when nd(u) = nd(v), where nd() returns node degree. 20 21 22 27 25 24 23 26
N(21)  N(22) and
nd(21)=3 < nd(22)=6
N(27)  N(22)
nd(27)=3 < nd(22)=6 id
nd(id)
N(id) 21 3
22,23,24 22 7
20,21,23,24,25,26,27 27
22,25,26
接著為base on node degree (ND)的方法
N[21]包含於N[22] 且N[27]包含於N[22] ,此外node21和node27的node degree小於N[22],所以根據Rule 3,node21和node27都會unmark他自己
Non-Gateway host
Gateway host
2017/4/24

69. Node-degree-based Approach (Rule 4)
Rule 4: Assume that u and w are two marked neighbors of marked vertex v in G . The marker v is unmarked if one of the following conditions holds:
Case 1. N(u)  N(v)  N(w), but N(v)  N(u)  N(w) and N(w)  N(u)  N(v) in G. 13 12
N(18)  N(11)  N(20)
but
N(11)  N(18)  N(20)
N(20)  N(11)  N(18) id
N(id) 11
4,12,13,15,16,17,18,20 18
11,17,19,20 20
11,18,19,22 15 11 16
Rule4第一個case
N[18]包含於N[11]∪ N[20], N[11]不包含於N[18]∪ N[20]且N[20]不包含於N[11]∪N[18]
也就是18,11,20中只有18能被其他兩個node取代,所以unmark node18 17 4 18 20
Non-Gateway host
Gateway host 19 22
2017/4/24

70. Node-degree-based Approach (Rule 4)
Case 2. N(u)  N(v)  N(w) and N(v)  N(u)  N(w), but N(w)  N(u)  N(v) in G; and one of the following conditions holds: (a) nd(u) < nd(v) (b) nd(u) = nd(v) and id(u) < id(v) 3 1 11 5 id
nd(id)
N(id) 2 8
1, 3, 4, 5, 6, 7, 8, 9 4 6
1, 2, 3, 9, 10, 11 9 7
2, 4, 5, 6, 7, 8, 10 2 4 6
Rule4第二個case
N[9]包含於N[2]∪ N[4], N[2]包含於N[4]∪ N[9],但N[4]不包含於N[2]∪N[9]
也就是9和2都能被其他兩個取代,但node9的 node degree較小故unmark node9 7 10 9 8
nd(9)=7 < nd(2)=8
N(2)  N(4)  N(9)
N(9)  N(2)  N(4)
but
N(4)  N(2)  N(9)
Non-Gateway host
Gateway host
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71. Node-degree-based Approach (Rule 4)
Case 3. N(u)  N(v)  N(w), N(v)  N(u)  N(w) and N(w)  N(u)  N(v) in G; marker u should be unmarked if one of the following conditions holds: (a) nd(u) < nd(v) and nd(u) < nd(w) (b) nd(u) = nd(v) < nd(w) and id(u) < id(v) (c) nd(u) = nd(v) = nd(w) and id(u) = min{id(v), id(u), id(w)} 14
id(13) < id(15)
nd(13) = nd(15) = 4
N(13)  N(11)  N(15)
N(15)  N(11)  N(13)
but
N(11)  N(13)  N(15) id
nd(id)
N(id) 11 8
4,12,13,15,16,17,18,20 13 4
11,12,14,15 15
11,13,14,16 13 12
Rule 4第三個case
N[13]包含於N[11]∪ N[15], N[15]包含於N[11]∪ N[13],但N[11]不包含於N[13]∪N[15]
也就是13和15都能被其他兩個取代,但node13和node15的 node degree一樣,故根據規則比較node id ,13的id較小,所以unmark node13 15 11 16
Non-Gateway host
Gateway host 17 4 18 20
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72. Energy-level-based Approach (Rules 5、6、7、8)
Energy-level-based rules
Let EL denote energy level
Rules 5, 6
Similar to rules 1 and 2, the only difference is to compare EL prior to node ID.
Rules 7, 8
Similar to rules 3 and 4
The only difference: when nodes u and v have the same EL, they compare ND prior to node ID.
接著為base on energy level (EL)的方法以增加網路lifetime
Rule 5,6大致跟rule 1,2一樣,唯一不同的是先比較剩餘電量(EL: energy level )當剩餘電量相同時, 才比較node id
Rule 7,8大致跟rule 3,4一樣,唯一不同的是先比較剩餘電量(EL: energy level )當剩餘電量相同時, 才比較NL : node degree,最後才比較id
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73. Conclusions Advantages Overall energy consumption is balanced
A relatively small connected dominating set is generated
優點:提升各node間電量的平衡,縮小connected dominating set
缺點:依然無法找出最小的connected dominating set
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74. Outline 5.1. Motivation and Goals
5.2. Power Control and Energy Conservation
5.3. Tree Topology
5.4. k-hop Connected Dominating Set
5.5. Adaptive node activity
5.6. Conclusions
2017/4/24

75. What’s Adaptive Node Activity?
Influence the topology of a graph by
Selecting certain nodes to be turned on or
Selecting certain nodes to be turned off
An operation that of course also fits well into the context of clustering or backbone mechanisms.
Nodes that are sources or sinks of data are always kept active
Adaptive Node Activity：
將拓樸圖形化後，分別決定哪些Node該醒、哪些Node該睡?
除了clustering及backbone外，Adaptive Node Activity也是一種不錯的網路拓樸控制機制。
下列兩種Node，恆為 active 狀態
資料來源 //資料持續傳送，直到資料傳送結束
Sink //持續接收資料
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76. Adaptive node activity
Geography-Informed Energy Conservation for Ad Hoc Routing
Y. Xu, J. Heidemann, and D. Estrin
ACM/IEEE MobiCom 2001
2017/4/24

77. Introduction Motivation Goal
Nodes consume high energy during routing, especially during transmission
Reduce the energy consumption in ad hoc wireless networks
Increase the network lifetime
Goal
Identifies equivalent nodes for routing
Based on location information
Turns off unnecessary nodes
Load balancing energy usage
Lifetime of all nodes remain as long as possible
[動機] 在Ad hoc網路中，Sensor nodes 除了一般感測、通訊與資料傳送工作外，還得額外耗費電力在感測器的移動。因此許多研究紛紛提出各種方法以減少 ad hoc 網路節點的電能消耗，增加網路的生命長度。
[目標] 本論文擬以感測器之醒睡機制(Adaptive node activity)建立網路拓樸，使網路能以分散式演算法決定感測器之醒睡，關閉網路多餘節點，增加網路生命長度。
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78. Geographical Adaptive Fidelity(GAF) Routing
Distribute routing duties by electing new local leaders periodically.
Leaders (active nodes) handle all routing traffic, allowing other nodes to sleep for extended periods of time and conserve energy.
Geographical Adaptive Fidelity(GAF) Routing
本論文提出 GAF Routing Protocol ，分散式地使網路中每個網格都能挑選出一個適合的 Active node ，負責自己所在網格的所有網路工作(感測、通訊、資料傳輸…)，並允許網格中的其他節點進入睡眠以減少電力消耗。
為了能讓每個節點負擔平衡，網格中的每個節點均有機會輪流擔任 active node，使得 load balanced。
網路中每個Grid均有自己獨立的醒睡機制(決定誰active, 誰sleep, and how long?)，使網路能以分散式演算法建立網路拓樸，達成增加網路生命長度的目標。
本方法適用於任何 ad hoc routing protocol
目標：使每個節點電能消耗平衡，延長網路生命時間。
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79. Determining Node Equivalence
The physical space is divided into equal size squares.
Based on radio communication range
Any two nodes in adjacent squares can communicate with each other.
In each grid, one node will stay in active state. r R 2r
Active node
Sleeping node
Source
Destination
r：the length of each grid
R：communication range of sensor node
為了使演算法能分散式的進行，先將網路場景依據感測器的通訊半徑切割網格(Grid)，且保證任相鄰Grid中的 sensor node 可互相通訊。網格的邊長 r 不大於1/√5倍的感測器通訊半徑 R。
因此，我們只需確保每個網格中都有一個 active node ，即能使網路以最少的電力正常運作 (sensing、communication、routing traffic…)。
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80. GAF State Transitions GAF consists of three states
Discovery: Due to mobility, node in this state aims to discover all nodes in the same grid
Active: In each grid, one node will stay in active state
Sleeping: In a grid, all nodes except the active node will stay in sleeping state
After Td
Discovery msg
After Ts
After Ta
Sleeping
Discovery
Active
GAF將感測器分為三種狀態：Discovery、Active與Sleeping State。
在Ad Hoc網路中，因感測節點具有移動性，節點於Discovery State會不斷地蒐集資訊，尋找自己所在的Grid中還有哪些其他節點，以便Grid中的每個節點能遵守相同的醒睡機制。
而進入 Active State 的節點將負責網路中所有工作，例如：感測、通訊、資料收送…等，並允許剩下的節點進入Sleeping State以減少電力消耗。
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81. GAF State Transitions Initially nodes start in the Discovery state
Node turns on its radio and find the other nodes within the same grid.
The node finish the discovery duration Td, broadcasts its discovery message (node id, grid id, estimated node active time, and node state) and enters Active state.
Td = random [0 ~ constant]
The other node switches its state into Sleeping state after receive the discovery message sentby the node which has higher rank value then itself. b
54% c a
92%
一開始每個節點都在 Discovery State，並不斷地尋找相同 Grid 中的其他節點。
經過一段時間 Td 後，節點廣播一個 discovery message 並進入 Active state。其中 discovery message 中包括該節點的ID、Grid ID、estimated node active time、和節點狀態。
為避免廣播 discovery message 時發生碰撞，Grid中的每個節點都會有不同的 Td 時間，Td 為一段隨機的時間，Td = random [0 ~ constant]。
當節點收到Grid中其他節點廣播的 discovery message，且發送該 discovery message 的節點Rank較高時，其他節點直接進入睡眠狀態。(意思就像是已經有等級比我高的節點要負起工作責任，那我就可以安心的進入睡眠狀態)
75% d
23%
　：sleeping state
　：discovery state
　：active state
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82. Node Ranking Rule Given any two node i and j
Ranki > Rankj , if and only if (enati > enatj)
enat = estimated node active time duration
(enlt = expected node lifetime)
, when enlt becomes less than a threshold
, when enlt larger than a threshold
決定Node的階級，讓最高階級的Node成為 active node
Node的階級依下列rule改變，使感測器電力負荷平衡
Active node的階級大於discovery node
Estimated node active time越長則階級越高
GAF使用Rank機制來控制Grid中的每個節點能公平的輪流進入active狀態，達到 load balance。
Grid中的每個節點會有不同的 rank value，而rank的高低取決於該節點期望active的時間長度(enat)：enat越多的節點，其rank越高，成為active node的機會也越高。
在正常狀況下，定義某個節點的enat為其剩餘電量的一半，使其他有較高剩餘電量的節點。
例如，一個剩餘電量還能使用2個小時的節點，希望她能夠active1個小時。但在節點電量過低的情況下，就直接讓她active到電量用完為止，因此enat=剩餘電量。
If node’s lifetime is less than a threshold, stay active state until energy exhaustion.
If node’s lifetime is larger than a threshold, balancing the remain energy to avoid frequent switches between active/sleep states.
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83. GAF State Transitions
A node in the Sleeping state wakes up after an application- dependent sleep time Ts, and switches its state into Discovery state.
Avoiding the active node leaving the grid and energy unbalance.
Ts = random [enat/2 ~ enat] b
Switches to Discovery state after Ts
54% c a
70%
92%
在Ad hoc網路中，因節點都具有移動性，可能隨時有節點移入或移出Grid，為避免Active node移出Grid，造成該Grid沒有Active節點，睡眠中的節點需不時的醒來偵測一下Grid中有沒有節點在工作。
因此，節點在睡眠一段隨機時間 Ts 後會變為 discovery state，重新蒐集Grid資訊。
而節點的睡眠時間 Ts = random [enat/2~enat]，會比節點 active 的時間短，就是為了犧牲一小部分的睡眠時間來避免網路空洞的發生。
75%
Energy drain d
Larger remain energy, higher rank
23%
　：sleeping state
　：discovery state
　：active state
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84. GAF State Transitions
The active node periodically rebroadcasts its discovery message
The active node leave active state:
After the time duration Ta = enat.
Receiving discovery message send by the other node which has higher rank value than itself. b
54% c a
70%
為了使Grid中的每個節點電力負荷能平衡，當Active Node剩餘電量低於其他節點時，將會被取代。
因此，節點會因下列兩種狀況離開Active State：
經過Ta時間，節點變回Discovery State
當節點收到Grid中其他節點廣播的 discovery message，且發送該 discovery message 的節點Rank較高時，則進入Sleeping State
75%
Receiving discovery message
Switches to Discovery state
Larger remain energy, higher rank
Broadcasts its discovery message
Become the active node d
23%
　：sleeping state
　：discovery state
　：active state
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85. Conclusions
GAF increases the network lifetime without decreases the performance substantially
Distribute routing duties by electing new local leaders periodically
All nodes remain up for as long as possible
本篇論文提出分散式的GAF Routing Protocol，以感測器之醒睡機制(Adaptive node activity)建立網路拓樸，使網路能關閉網路多餘節點，增加網路生命長度。
GAF方法增長了網路的生命時間
並不會因此減少傳遞的效能
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86. Conclusions
Various approaches exist to adjust the topology of a network to a desired shape
Most of them produce some non-negligible overhead
Some distributed coordination among neighbors require additional information.
Constructed structures can turn out to be somewhat brittle and the overhead might be wasted.
Benefits have to be carefully weighted against risks for the particular scenario at hand
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87. References
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N. Li, J. C. Hou, and L. Sha. Design and Analysis of an MST-Based Topology Control Algorithm. In Proceedings of IEEE INFOCOM, San Francisco, CA, March 2003
J. Wieselthier, G. Nguyen, and A. Ephremides, On the Construction of Energy-Efficient Broadcast and Multicast Trees in Wireless Networks, in Proc. IEEE Infocom’2000, Tel Aviv, Israel, pp. 585–594, 2000
Jie Wu, Fei Dai, Ming Gao, and Ivan Stojmenovic, On Calculating Power-Aware Connected Dominating Sets for Efficient Routing in Ad Hoc Wireless Networks, Journal of Communications and Networks, vol. 4, No. 1, march 2002
B. Chen, K. Jamieson, H. Balakrishnan, and R. Morris. Span: An Energy-Efficient Coordination Algorithm for Topology Maintenance in Ad Hoc Wireless Networks. Wireless Networks, 8(5): 481–494, 2002
Y. Xu, J. Heidemann, and D. Estrin. Geography-Informed Energy Conservation for Ad Hoc Routing. In Proceedings of the 7th Annual International Conference on Mobile Computing and Networking (MobiCom), pages 70–84, Rome, Italy, July ACM.)
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